## Alternative for (A8+3A2)+A4+A1 (nt83)
Read("GAP.txt");
beta  := [s3^-1, s2^-1, s1^-1*s3^-3, s2^-2, s1^-1];;
gamma := [s2^-1*s1*s3^-1*s2, \1, \1, s2^-1*s3, \1];;
braid := [s3^3, s2^2, s1^2*s3^5, s2^5, s1];;
K := 3;;
kappa := a1*a2;;
g_im := \1;;
gamma_im := s2*s1^-1*s3*s2;;  # manually
rel_K := [a1*a2*(a3*a4)^2, a4*(a3*a4)^4/((a3*a4)^4*a3)];;  # manually
## Perturbations:
#: The $A_4$ point
braid := [s3^3, s2^2, s1^2*s3^5, s2, s1];;
init_group(3: Simplified);
rels;
qsize(g.1/g.2);
#> 6  ## This is the commutant!
simplify(g.1/g.2);
#> #I  there are 2 generators and 0 relators of total length 0
